That's the whole point. We think the Distributed Web is cool and coming and we want to accelerate that happening. Hence the time and effort to make this happen.
That was one of the drivers. We liked the core technology, but could see there was a significant barrier to actually using it. Being able to point your domain at IPFS content and then providing that (ssl secured) site to the masses is a big step forward.
We wrote a tutorial on setting it up on your own (secure nginx server for ipfs gateway), https://medium.com/textileio/tutorial-setting-up-an-ipfs-pee.... But for sure, for most users, going right through cloudflare is an awesome simplification. Exciting stuff.
You can use any gateway with your custom domain name? Potentially you could but I don't know of any that let you do this.
My impression of the public gateways was that the end user would need to know the content hash of your website which makes for a poor user experience.
This announcement claims the end user just uses the website as they normally would by visiting example.com but behind the scenes there is no central web server because the content is pulled from IPFS.
I was running my own website with my own domain on ipfs quite successfully for few months. And I have configured cloudflare just to have a green https icon.
The only problem is that I have to visit my website once in a while, otherwise the content is deleted on the gateway.